Thursday, 28 March 2019

On giant mecha - how practical are they?


You know exactly what I am talking about. You've probably run into them at some point, be it through films or some form of animation. This article will be about their practicality, with current technology.

So, first things first, can it stand?


Let's look at some figures.
The tire pressure of an aircraft is the pressure it exerts on the ground (the surface area of the tire in contact with the ground changes depending on the weight of the aircraft, keeping the pressure constant). For most commercial aircraft, it's about 200 psi - or 1 379 000 pascals (Newtons per square meter, approximately 137 900 kg per square meter of tire surface). This is designed for the hard surface of runways and taxiways in an airport - such an aircraft can't land on soft ground and not sink into the ground at least and little.
The ground pressure (as it is called), for more everyday things - like humans - is a lot lower. A human exerts about 55 000 pascals when standing, though this can more than twice that when walking / running (source: wikipedia). A passenger can exerts about 205 000 pascals. A mountain bicycle exerts about 245 000 pascals, while a road racing bike exerts about 620 000 pascals. A stiletto heel can exert as much as 3 250 000 pascals - more than an aircraft (which is why they damage floors and many other surfaces).

Let's see what this translates to. If the ground pressure is to be the same as that of a normal vehicle, a 100 tonne mecha would have to have a surface area of (100 x 1000 x 10)/(205 000) = 4.878 m2 in contact with the ground. To stand on 1 foot (and walk), this would require a foot that is about 2 m wide and 2.43 m long. For one that's half that weight, the required area of the foot would be half of that (about 1.5 m x 1.62 m).This is assuming that pressure is distributed fairly evenly by the foot, which is highly unlikely unless it has a rubber sole (which would immediately make kicks about one third as cool). Chances are, if the mecha are made like humans, more weight would be concentrated on the back of the foot.

Still, according to these calculations, a mecha would probably be able to stand on most surfaces.

Part II - can it not collapse under its own weight?

A major issue we face here is the square-cube law: doubling an object's dimensions, which multiplies its surface area by a factor of four, also increases its mass by a factor of eight. This is a problem, because properties like tensile and compressive strength depend on an object's cross-sectional area. So, when you increase it's strength by a factor of 4, you increase its mass by a factor of 8, which means you need more strength to support the increased weight.

Let's compare some comparable structures.

Falcon 1 rocket: Height: 21.2 m, Diameter: 1.7 m, Mass: 27.67 tonnes (source)
Boeing 747-8: Length: 76.25 m, Wingspan: 68.4 m, Mass (Operating empty weight): 220.128 tonnes (source)
Rockwell B-1 Lancer: Length: 44.5 m, Wingspan: 24 m - 42 m (swing wing), Mass: 87.1 tonnes (source)
Falcon 9 rocket: Height: 70 m, Diameter: 3.7 m, Mass: 549.054 tonnes (source)

I chose the Rockwell B-1 Lancer as an example because it includes a rather large moving part - the wing sweep can be changed in flight.

As you can see, chances are, an average mecha will not crumble under its own weight - if it was standing still. So, you can build a statue of it without a problem. However, that is not what we want, we want it to be able to move, to run, to shoot lasers, and to kick other mecha in the face.

So, it needs to move...


Therein lies the problem. To accelerate a part as heavy as a mecha's legs, you are going to need some very powerful motors. For a 20 m, 50 tonne robot, we can assume that its legs are about 10 m tall - approximately half its height. If one third of its weight is in its legs, and the centre of gravity of the leg is one third of the way down the leg from the hip (both are probably conservative estimates), to swing the robot's leg, you will need a torque of (10/3)*((50 000*10)/3) = 555.56 kNm. A 100 kNm motor looks like this (look at the images this page).

In addition to that, to accommodate all that movement, the legs will have to be strong. As in, it should be able to handle being swung at something at high speed, with something heavy attached to the end of it (the foot, the lower leg, and the knee joint, and all associated actuators/sensors) without bending in the middle.

But I got ahead of myself. In order to kick something in the face, the mecha has to reach said target, and if it is, indeed, terrestrial, it has to walk or run there. Walking can be rather complex. One foot has to be taken off the ground, while the weight balances on the other momentarily, and when that foot reaches the ground, the weight must be transferred to it in order to move the other leg. Running can be more taxing still - the mecha has to generate enough force for both feet to leave the ground temporarily. Besides, running exerts a lot of force on the ground (Newton's third law).

All this means a lot of bending moment on the legs, as it balances the body over the heel like an inverted pendulum. To counter this, you need very strong materials for the legs. If you want it to stand on the ground without turning a paved road into quicksand, and if you want reasonable sized motors / actuators, you will need a light-weight material. There are few materials that meet both these requirements.

Provided we found the right material, we still have to move the individual joints. We will need fairly large motors if we are going to use motors. These motors would probably need a lot of current, which introduces a host of other problems (motor control becomes more difficult, and the wires get thicker and heavier, among other things) Another viable option is hydraulics, which will also be very large and very heavy. You will also need a full hydraulics system if you select this option, which also translates to more weight,complexity, and issues with materials. In either case, the actuator we use must be fast,responsive, and very controllable. Finding or manufacturing such actuators will not be easy.

Power?


In order to do all of this, we need a source of power. Given the space constraints and the energy requirement, nuclear might be the only really viable option, but the reactor size will probably have to decrease a little. Power isn't my area of expertise, so I can't say for sure, but I don't think the technology is there quite yet.

Controllability

And now, my favourite part the discussion - how do you make the robot work?

First, you will need to know the robot's starting configuration - how the limbs are positioned, the robot's posture, whether it's stationary or moving, etc. For this, you will need sensors, and a lot of them. You will need to know the position of each motor. You will need to know the tension on the leg beams. You will need accelerometers and gyroscopes, probably in each limb, to measure current linear and rotational acceleration. All this is available, so there is no problem there.

The next problem is judging where the robot is going to step. You can use a radar to map the contours on the ground, and you could also use images from one or more cameras to help you. A laser scanner could also help, but it could be overkill in this case. Again, we have the technology - it's expensive, and difficult to implement, but we definitely have the technology. If there is any problem here, it's creating a transparent window through the foot to get the images necessary.

This information has to be processed. That shouldn't be too hard, but a possible issue is time delays. Chances are, all control will be by a central processor, which will command lower level processors in the limbs, etc, at a high level (at least, that is the design that makes the most sense to me). In order to get it to walk, the arms, legs, torso, and head movements must be coordinated. Delays in transmitting main control commands could potentially throw the whole system out of sync if the problem is bad enough. If the feedback from the limbs, etc. are delayed, or if the data from those sensors are gibberish, that could cause a problem as well. Also, there is the problem of sensors producing readings at different rates, which can be dealt with, but it can cause problems. The long distances can make data transmission errors more likely, but that can be dealt with.

The next problem is the actuators themselves. If my experience teaches me anything, it is that this part is going to be ridiculously difficult. As I mentioned before, finding motors or other actuators that are powerful enough and quick enough would be difficult. I can't be certain about hydraulics, but with motors, controlling it is going to be difficult because finding a motor control circuit that is small enough, and won't heat too much (or burn out) with intermittent operation would be nearly impossible. The other problem is managing space when installing them (though hopefully that wouldn't be too much of a problem with hydraulics.

To summarize,

Sensing and data processing can be done - it won't be easy, but it can be done.
If you can build it, it will be able to walk without sinking a couple of metres into the ground with each step.
Finding material that can be used to build it will be a problem.
Finding a power source is likely impossible right now.
Finding suitable actuators would be very difficult.

The verdict: It's not possible right now, but maybe it will become a reality in the near future. It might not have any practical use, but it'll be an interesting experiment for nerds like us.

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Until next time!

1 comment:

On giant mecha - how practical are they?

You know exactly what I am talking about. You've probably run into them at some point, be it through films or some form of animation. T...